The TOC in the article class is formatted as a section. In memoir it is a chapter by default. I would prefer to have the TOC formatted in such a way that its heading gets formatted with the same font (smaller) and distance (closer) to what follows as a section would.
An example with memoir:
\documentclass{memoir}
\usepackage{lipsum}
\begin{document}
\chapter{Name of my Article}
\tableofcontents*
\section{A Section}
\lipsum{}
\subsection{A Subsection}
\lipsum{}
\end{document}
And a roughly equivalent example using article:
\documentclass{article}
\usepackage{lipsum}
\begin{document}
\title{Name of my Article}
\maketitle
\tableofcontents
\section{A Section}
\lipsum{}
\subsection{A Subsection}
\lipsum{}
\end{document}
\chapter{Name of my Article}
indicvates that you are using this completely wrong. Use\title{Name of my Article}
along with\maketitle
and the global optionarticle
to typeset an article, not a bigger report/book.